A292773 a(n) is the least integer m such that any choice of m elements in (Z_3)^n contains a subset of size 3 whose sum is zero.
5, 9, 19, 41, 91, 225
Offset: 1
Links
- Y. Edel, C. Elsholtz, A. Geroldinger, S. Kubertin and L. Rackham, Zero-sum problems in finite abelian groups and affine caps, Quarterly Journal of Mathematics 58 (2), 159-186.
- Christian Elsholtz, Lower bounds for multidimensional zero sums, Combinatorica 24.3 (2004): 351-358.
- H. Harborth, Ein Extremalproblem für Gitterpunkte, J. Reine Angew. Math. 262 (1973), 356-360.
- Aaron Potechin, Maximal caps in AG (6, 3), Designs, Codes and Cryptography volume 46, pages 243-259 (2008).
Crossrefs
Cf. A090245.
Formula
a(n) = 2*A090245(n) + 1, (follows from Harborth, Hilfssatz 3). - C. Elsholtz, Oct 04 2021
Extensions
a(6), based on Potechin's paper, added by C. Elsholtz, Oct 04 2021